Problem: Rewrite as a simplified fraction. ${0.3\overline{64} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 364.6464...\\ 10x &= 3.6464...\end{align*}}$ Subtracting the two equations, we have: ${990x = 361}$ ${x = \dfrac{361}{990}} $